# Moment of inertia and turning performance

Smooth turning has been a challenge for our robot this year. We noticed that unlike our 6-wheel tank drivetrain, several teams have been able to create 6WD with butter-smooth turning. We recognized that our off-center CG degraded our turning abilities. However, I feel that there should be another cause that adds to the “jumpiness” of our turns. My prime suspect is the moment of inertia, both about the turning axis and the middle wheels. Suppose that you have a robot with a fairly well-centered CG. Will large or small moment of inertia about the turning axis result in smoother turning performance?

The moment of inertia for the robot is a complex system. (Assuming from here a simple normal system) A low moment of inertia results in a lower rotational momentum and therefor a greater ability to start and stop turning. A high moment of inertia results in a higher rotational momentum and therefor a greater desire to keep turning at the same rate.

If you only want to have a consistent, smooth turn, a high moment of inertia is what you want BUT at the cost of responsiveness and control.

also keep in mind that your CG is only ideally placed when centered if your robot turns exactly around the CG.

Finally: the choppy turning may be because of your programing or your power transfer method.

Usually it’s a matter of traction vs. center wheel drop. If you have a bit too much traction, or not enough center wheel drop, then it’s kind of hard to turn.

My guess is moment of inertia plays a very minor role.

The biggest factors affecting turning for a drop-center 6WD are

• amount of drop of the center wheels

• type of flooring

• wheelbase/trackwidth ratio

• location of center of mass

For wheels having similar traction, wheelbase length is the primary factor in how easily a robot turns. The two typical ways to eliminate bouncy turns on a 6-wheel drivebase are to 1) get the center of mass directly over slightly-lowered center wheels, and 2) use omniwheels at the corners to remove friction in the sideways direction.

No lie. At last year’s inspection, we weighed in a tiny bit over the weight limit. Me, wanting to tidy the robot, trimmed all the ends of the zipties we used and, miraculously, we weighed in exactly at 120 pounds!

We used a lot of zip ties that year…

Last year we had problems with our 6 wheel kitbot drive. The center wheel wasn’t dropped enough, so pretty much all 6 wheels were on the ground. It was extremely jumpy and hard to turn. We solved this in the offseason by switching to the grip wheels in the rear, powered, removing the middle wheels all together, and throwing free spinning omnis on the front. Worked great. And we learned our lesson, this year we have an 8wd that drives like a beast.

We usually do a 6wd with a 1/8 inch drop center and roughtop tread on all wheels. Our robots always turn smooth as silk but this years robot didn’t turn well at all. I think our weight was too centered over the middle wheels. we were able to bolt a 7 pound weight to the back of the robot which completely cured it. With a 1/8 drop center those front wheels are really close to the carpet and I think you need to keep them from grabbing as much as possible for smooth turning.

The prime suspect for a ‘jumpy’ 6 wheel drivetrain would be a combination of traction materials and CG in relation to the center wheels. Also, it’s possible for a small center drop to be overwhelmed by the frame flexing enough to allow the corners wheels to see more weight then is ideal.

However there are instances where turning problems can be related to control setup or PID loop tuning, and not just hardware. Are you using a PID loop on your drive train? Are you using one joystick drive? Two? A gamepad? Simple mistakes in the axis mixing or PID terms can result in really wonky turning behavior.

It can also be helpful, though not at all necessary, to use Jaguars on drive motors. They have slightly better performance that can help improve turning at low speeds. The victor/jaguar thing is still a touchy subject, I know, but this is one thing the jags really do have going for them.

Our team has done a lot of personal testing and evaluation on the top teams in the league and we have found that the CoG and tortional stiffness is generally what sets their robot’s drivetrain apart from most others.

CoG, contrary to popular belief we have found that setting the CoG far to one side on a 6wd is best. A 6wd performs best when it is actually a 4wd with 2 extra wheels. Placing the CoG in the middle generally results in the turning point of the robot changing in the middle of the turn as the robot accelerates/decelerates and the outer wheels alernating touching the ground. This is especially important because a 6wd does not turn about the middle wheels but rather between the middle wheels and whichever pair of outer wheels happens to be touching the ground. So by limiting rocking as much as possible performace greatly increases.

Tortional stiffness is absolutely critical to a good 6wd. In 2008 we discovered that without a very stiff chassis the opposite outer wheels will touch down essentially creating a long wheelbase while turning. This will also seriously limits turning.

Edit: I forgot to add, an 8wd has mathmatically much better turning characteristics than a 6wd provided the wheels are properly spaced.

But don’t take my word for it, if you don’t believe me run some experiments.
Regards, Bryan

From watching a few of your matches on youtube, the symptoms (rocking “hops” when turning, with size of rock roughly proportional to speed of turn) seem very much like those of a drivetrain with too much resistance to turning, the result of having too much traction at the corners of a drivebase with a long wheelbase and narrow track.

Some ways to reduce this issue:

• Reduce traction at corners by:
• Making corner tires less grippy (slick wheels, or something less extreme)
• Making corner tires move sideways easily (90 degree omnis)
• Reducing weight on corners (increasing “rocker” and/or stiffening frame so that sag doesn’t eliminate “rocker”)
• Reducing weight on corner wheels by centering weight over center wheels
• Shorten wheelbase and/or widen track to get a footprint more advantageous for turning

I wouldn’t recommend a rocker greater than 1/8"… If putting the center wheels 1/8" lower isn’t sufficient, look at your frame sag. Then consider the lateral grippiness of your corner tires and where your CoG is.

Note that you don’t want the robot to turn without any resistance, as it’d be nearly uncontrollable; however, you don’t want so much resistance that you’re hopping at even fairly low-speed turns… Some teams prefer just using omnis at the corners, while others prefer using rocker, or a more advantageous wheelbase/track ratio. Personally, I prefer a combination of the rocker, CoG, and wheelbase/track ratio to provide a drive base that goes straight naturally but still turns well and won’t be spun around by a defender.

Building on what Bryan said…

CoG is a very overlooked thing in 6WD/8WD design. Its important to really consider where the approximate CoG of your robot will be as its being designed. This becomes especially true as you begin to build taller structures on top of your drive system. Weight higher up will tend to amplify the issues you are seeing with turning performance.

-Brando

Torsional stiffness and a low CoG are absolutely critical to smooth turning in a dropped-center, skid steer drivetrain.

Segways turn without any* resistance.

A 6WD with omnis at all four corners is like a Segway with training wheels.

*well, for all practical purposes

Our robot was symmetrical this year. Well, not exactly symmetrical, but so much so that our driver has trouble telling one end of the robot from the other. We are using 6wd off a CIM and a FP a side. All 6 wheels are 6in performance wheels with blue nitrite tread, and the center wheels are dropped about an eighth of an inch.

We turn very easily, at least much more easily than most 6wd robots with all traction wheels. However, if you watched our robot play, you would say that it turned very jerkily. Why? The driver and the programming.

This is merely an explanation for why a LOW c.g. matters.

Consider a c.g. that’s off-center to the right and is 18" off the ground (really high for FRC). When moving forward, that c.g. creates a moving inertia. During a sweeping left-hand turn while moving, that inertia becomes a centrifugal force that attempts to lift the left side of the robot. The higher the c.g., the more leverage the force has to lift the left side. This centrifugal force is easily noticable on robots that do high-speed 0-radius turns in place. It’s like an off-balanced top.

This lifting causes a major traction loss, even if it only lifts a few tenths of an inch. Realize that with even a few degrees of lateral lift, a wheel that makes flat contact with the field (such as the KOP wheels) will lose nearly all of its traction. Rounder wheels, like the AM pneumatic wheels, will only lose some of their traction. This traction loss is why high c.g. robots cannot do sweeping turns like the more agile robots. A good picture of this concept is on page 41 of this slide deck: http://www.chiefdelphi.com/media/papers/2597

I’m assuming that you are implying that you do often want a drive train that turns with negligible resistance, and that they can be controllable?

In the “real world” (i.e. with cars, airplanes, segways, etc.) you’re definitely right - you basically always want no mechanical resistance in the drive mechanism. As a result, you have a drive mechanism that is capable of being quite responsive. However, if that mechanism is controlled carelessly, it could result in a vehicle that responds easily to accidental maneuvers. These potential side-effects are mitigated by control mechanisms with resistance or “feedback” (such as the yoke or stick on a plane), control motions that aren’t inherently twitchy (two hands on a reasonably sized steering wheel), software damping of otherwise twitchy motions (a Wii uses some of this, I conjecture), and/or by training the manipulator to use the responsive mechanism advantageously (fighter pilot).

These are all better ways of getting good controlability out of an otherwise difficult-to-control system; however, I made several unspoken assumptions when I thought what I wrote. I figured teams would be working with control mechanisms that aren’t perfect (the current joysticks at least have a little more resistance than the old ones…), that they’d be using control motions that aren’t always easy to make steady (unsupported arms on two different joysticks), that most teams wouldn’t be using software to damp out twitchiness (perhaps some teams do), and that teams wouldn’t be requiring a level of responsiveness that could only be acquired with a resistance-free mechanism.

From our own team’s experience, our drivers had a hard time getting accustomed to our very low-resistance drive trains… but we ended up with robots that could drive fairly well by compensating. We didn’t want all the responsiveness we had, so we used software to map the distance from the neutral axes exponentially, so that small motions would be less significant. I consider this raising the tolerances, rather than “damping out twitchiness…” which I presume would be feasible but significantly more difficult, and perhaps not even preferable. We also used software so that when the driver hit a button they could limit the robot to half (or quarter) power for fine motions, such as placing a tube on a peg last year or lining up for a shot in 2010. Then we got the drivers to practice a lot.

So, in the FRC robot world, my experience has been that a hyper-sensitive robot is not preferable and that a good way to limit the sensitivity is to leave a little resistance in the system (i.e. put grippy tires at the corners rather than omnis); however, some teams may think otherwise. Perhaps your team disagrees… I could imagine some teams preferring hyper-sensitive robots that are driven well solely by the skill and practice of their drivers…

I apologize for my non-absolute statement that could easily be misinterpreted.

I think your expanded explanation makes a lot of sense.
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Have you ever tried to turn an active Segway by manhandling it instead of using the steering control? It has plenty of resistance. Granted, it’s mostly due to software controlling the wheels and not to strictly mechanical tendencies.

I think it would be better to say that a Segway has very little wheel scrub to worry about.